If a = –2 – 5i and b = –i, then find the value of the ab^3 in fully simplified form.

5 + 2i

We were given the complex numbers;

a = - 2 - 5i

and

b = - i

We want to find the product;

ab^3                            ^ = Exponent

We substitute the complex numbers into the expression and simplify

( - 2 - 5i ) (i)^3                     ^ = Exponent            

This is rewritten as:

( - 2 - 5i) (i)^2     x  i                           ^ = Exponent

Note that

i^2 = - 1                                            ^ = Exponent

We substitute to obtain:

( - 2 - 5i )  x  - i                

Let us expand to get:  

- 2 x - i + 5i  x  - i

This simplifies to:

2i - 5i^2                           ^ = Exponent

This gives:

2i - 5 ( - 1 ) = 2i + 5

Hope This Helps

DOH! My Brian Hurts

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

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step-by-step explanation: